Finite Group Databasebeta

← #28374800

Subgroups — #28374800

Order 13952.

464 conjugacy classes of subgroups; only the 117 normal subgroups are shown.

normal subgroups only

This group has 464 conjugacy classes of subgroups — too many to draw. Only its 117 normal subgroups are shown.

Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#20295834C212yesmaximal, complemented
2#20295830C212yesmaximal, complemented
3#20295416C211yesmaximal, characteristic, complemented
4#20295294C212yesmaximal, complemented
5#20295292C212yesmaximal, complemented
6#20295203C211yesmaximal, characteristic, complemented
7#20295195C212yesmaximal, complemented
8#20295145C212yesmaximal, complemented
9#454×C109C211yesmaximal, characteristic, complemented
10#16812745C2212yescomplemented
11#16812744C2211yescharacteristic
12#16812730—22no—
13#16812730C2212yescomplemented
14#16812727C2212yes—
15#16812726—22no—
16#16812724—22no—
17#16812724C2212yescomplemented
18#16812723—22no—
19#16812720—22no—
20#16812719—22no—
21#16812719C2212yes—
22C2×#13182016—22no—
23C2×#13182016C2212yescomplemented
24C2×#13182014C2212yescomplemented
25D8×D109—22no—
26#16812707C2212yescomplemented
27#16812706C2212yescomplemented
28#16812696C2211yescharacteristic, complemented
29#16812634C2212yescomplemented
30#16812627C2212yescomplemented
31#16812616C2211yescharacteristic, complemented
32#16812615C2212yescomplemented
33#16812610C2211yescharacteristic, complemented
342−1+4×C109C2211yescharacteristic, complemented
35AGL(1,ℤ/8)×C109C2212yescomplemented
36#124×C109C2211yescharacteristic, complemented
37#104×C109C2212yescomplemented
38#101×C109C2211yescharacteristic, complemented
39#13182030—22no—
40#13182029—22no—
41#13182029C2312yes—
42#13182028—22no—
43C2×D436—22no—
44C2×D436—41no—
45C2×D436C2312yes—
46C2×C22⋊D109—41no—
47D4×D109—22no—
48D4×D109—22no—
49D4×D109—42no—
50#13182019—22no—
51#13182019D412yescomplemented
52#13182018—22no—
53#13182017D412yescomplemented
54#13182016—22no—
55#13182016—22no—
56#13182016—22no—
57#13182016—22no—
58#13182016D412yescomplemented
59D872—22no—
60#13182014—22no—
61#13182014—22no—
62#13182014—22no—
63#13182014D412yescomplemented
64#13182013—22no—
65#13182013C2312yes—
66#13182012—22no—
67C2×#11724784—22no—
68C2×#11724784C2312yes—
69C8×D109—22no—
70#41×C109—22no—
71#41×C109—41no—
72#41×C109C2312yes—
73C2×Q8×C109—22no—
74C2×Q8×C109C2311yescharacteristic
75C2×D4×C109C2311yescharacteristic
76SD16×C109—22no—
77D8×C109—22no—
78M16×C109C2312yes—
79C22⋊C4×C109—41no—
80C42×C109C2311yescharacteristic
81C23×C109—21no—
82C22×D109—22no—
83C22×D109—41no—
84C22×D109—42no—
85Q8×C109—22no—
86Q8×C109—41no—
87Q8×C109C2×D412yes—
88D4×C109—22no—
89D4×C109—22no—
90D4×C109—41no—
91D4×C109C2×D412yes—
92C2×C4×C109—22no—
93C2×C4×C109—21no—
94C2×C4×C109—21no—
95C2×C4×C109—42no—
96C2×C4×C109C2411yescharacteristic
97C22⋊D109—22no—
98C22⋊D109—42no—
99C22⋊D109—42no—
100C2×Dic109—41no—
101D436—22no—
102D436—22no—
103D436—42no—
104D436—82no—
105D436C2×D412yes—
106C4×D109—22no—
107C4×D109—42no—
108Dic218C2×D412yes—
109C8×C109—22no—
110#11724784—22no—
111#11724784C2×D412yes—
112#11724784C2×D412yes—
113C22×C109—22no—
114C22×C109—41no—
115C22×C109—81no—
116C22×C109H(5,𝔽2)11yescharacteristic
117C2×D109—22no—
118C2×D109—42no—
119C2×D109—82no—
120C2×D109—161no—
121C2×D109—162no—
122C4×C109—22no—
123C4×C109—41no—
124C4×C109—41no—
125C4×C109C22×D412yes—
126Dic109—22no—
127C2×C109—21no—
128C2×C109—42no—
129C2×C109—81no—
130C2×C109D4211yescharacteristic
131D109—42no—
132D109—82no—
133#3288—1091nomaximal, Sylow
134C109#328811yescharacteristic, complemented, Sylow
135#577—1092no—
136#576—1092no—
137#496—1091no—
138#472—1092no—
139#471—1092no—
140#455—1091no—
141#454D10911yescharacteristic, complemented
142#453—1092no—
143#444—1092no—
1442−1+4C2×D10911yescharacteristic, complemented
145H(5,𝔽2)—1092no—
146H(5,𝔽2)—1091no—
147#137—1092no—
148#137—2182no—
149AGL(1,ℤ/8)—1092no—
150AGL(1,ℤ/8)—1092no—
151AGL(1,ℤ/8)—2182no—
152AGL(1,ℤ/8)—2182no—
153AGL(1,ℤ/8)—2182no—
154AGL(1,ℤ/8)C2×D10912yescomplemented
155#135—1092no—
156#135—2182no—
157#135—2182no—
158C2×SD16—1092no—
159C2×SD16—2182no—
160C2×D8—1092no—
161C2×D8—2182no—
162#131—1092no—
163#131—1092no—
164#127—1091no—
165#124C2×D10911yescharacteristic, complemented
166#108—1092no—
167#104—1092no—
168#104C2×D10912yescomplemented
169#101C2×D10911yescharacteristic, complemented
170#100—1091no—
171#100—1092no—
172#97—1091no—
173#41—22no—
174#41—41no—
175#41—1092no—
176#41—2182no—
177#41—2182no—
178#41—2182no—
179#41C22×D10912yes—
180C2×Q8—22no—
181C2×Q8C22×D10911yescharacteristic
182C2×D4—1092no—
183C2×D4—4361no—
184C2×D4—4362no—
185C2×D4—4361no—
186C2×D4—2182no—
187C2×D4—2182no—
188C2×D4—2182no—
189C2×D4C22×D10911yescharacteristic
190Q16—1092no—
191Q16—2182no—
192SD16—22no—
193SD16—1092no—
194SD16—1092no—
195SD16—2182no—
196SD16—2182no—
197SD16—2182no—
198SD16—2182no—
199SD16—2182no—
200D8—22no—
201D8—1092no—
202D8—2182no—
203D8—2182no—
204D8—2182no—
205D8—2182no—
206M16—1092no—
207M16—2182no—
208M16—2182no—
209M16C22×D10912yes—
210C2×C8—1092no—
211C2×C8—2182no—
212C2×C8—2182no—
213C22⋊C4—41no—
214C42C22×D10911yescharacteristic
215C23—21no—
216C23—4362no—
217C23—4361no—
218C23—2182no—
219Q8—22no—
220Q8—41no—
221Q8—1092no—
222Q8D4×D10912yes—
223D4—22no—
224D4—22no—
225D4—41no—
226D4—8722no—
227D4—1092no—
228D4—4362no—
229D4—4362no—
230D4—4362no—
231D4—2182no—
232D4—2182no—
233D4—2182no—
234D4D4×D10912yes—
235C2×C4—22no—
236C2×C4—21no—
237C2×C4—21no—
238C2×C4—42no—
239C2×C4—4362no—
240C2×C4—4361no—
241C2×C4—2182no—
242C2×C4C23×D10911yescharacteristic
243C8—22no—
244C8—1092no—
245C8—1092no—
246C8—2182no—
247C22—22no—
248C22—41no—
249C22—81no—
250C22—8722no—
251C22—4362no—
252C22—17442no—
253C22—17441no—
254C22—2182no—
255C22#1681274411yescharacteristic
256C4—22no—
257C4—41no—
258C4—41no—
259C4—2182no—
260C4C2×D4×D10912yes—
261C2—21no—
262C2—42no—
263C2—81no—
264C2—8722no—
265C2—4362no—
266C2#2029565811yescharacteristic
subgroupG/H
centerC2#20295658
commutator, cosocleC2×C4×C109C24
FrattiniC2×C4C23×D109
Fitting#454×C109C2
socleC2×C109D42
hypercenter#454D109
hypocenterC109#3288
LCSG ▷ C2×C4×C109 ▷ C2×C109 ▷ C109
UCSC1 ◁ C2 ◁ C2×C4 ◁ #454

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

NH ≅ G/Ntype
1. #20295834C2semidirect
2. #20295830C2semidirect
3. #20295416C2semidirect
4. #20295294C2semidirect
5. #20295292C2semidirect
6. #20295203C2semidirect
7. #20295195C2semidirect
8. #20295145C2semidirect
9. #454×C109C2semidirect
10. #16812745C22semidirect
13. #16812730C22semidirect
17. #16812724C22semidirect
23. C2×#13182016C22semidirect
24. C2×#13182014C22semidirect
26. #16812707C22semidirect
27. #16812706C22semidirect
28. #16812696C22semidirect
29. #16812634C22semidirect
30. #16812627C22semidirect
31. #16812616C22semidirect
32. #16812615C22semidirect
33. #16812610C22semidirect
34. 2−1+4×C109C22semidirect
35. AGL(1,ℤ/8)×C109C22semidirect
36. #124×C109C22semidirect
37. #104×C109C22semidirect
38. #101×C109C22semidirect
51. #13182019D4semidirect
53. #13182017D4semidirect
58. #13182016D4semidirect
63. #13182014D4semidirect
134. C109#3288semidirect
141. #454D109semidirect
144. 2−1+4C2×D109semidirect
154. AGL(1,ℤ/8)C2×D109semidirect
165. #124C2×D109semidirect
168. #104C2×D109semidirect
169. #101C2×D109semidirect

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroupindex
#202958342
#202958302
#202954162
#202952942
#202952922
#202952032
#202951952
#202951452
#454×C1092
#3288109